What is the pH of a solution containing 0.05 M atropine sulfate solution and 0.5 M atropine solu

step 1 So this question asks you, what is the pH for 0 .045M, a weak base, okay, a weak base with KB 4

What is the pH of a solution containing 0.05 M atropine...

What is the $\mathrm{pH}$ of a solution containing $0.05 \mathrm{M}$ atropine sulfate solution and $0.5 \mathrm{M}$ atropine solution in one-liter, using the $\mathrm{K}_{\mathrm{b}}$ of atropine as $4.47 \times$ $10^{-5}$ at $15^{\circ} \mathrm{C}$ ?

Key Concepts

Relationship Between Kb and Ka

For a conjugate acid-base pair, the ionization constants Kb (for the base) and Ka (for the conjugate acid) are related by the water ionization constant Kw (Ka × Kb = Kw). This relationship allows conversion between pKa and pKb values, which is essential when applying the Henderson–Hasselbalch equation in the context of a buffer made from a weak base and its conjugate acid.

Henderson–Hasselbalch Equation

The Henderson–Hasselbalch equation is a simplified relationship derived from the acid-base equilibrium expression. It is used to estimate the pH of buffer solutions by relating the pH to the pKa and the ratio of the concentration of the conjugate base to the acid (or for a basic buffer, relating pOH to pKb and the ratio of acid to base). This equation is particularly useful for calculating the pH of mixtures where a weak base and its conjugate acid are both present.

pH and pOH

pH is the measure of the hydrogen ion concentration in a solution, indicating its acidity or basicity. Understanding pH involves knowing that lower values indicate acidic solutions and higher values indicate basic ones. In the context of acid-base equilibria, pH is calculated either directly from [H?] or indirectly by first calculating pOH from the hydroxide ion concentration and then using the relation pH + pOH = 14 at 25°C (adjusted if the temperature is different).

Weak Base Equilibrium

A weak base does not completely dissociate in water; instead, it reacts with water to establish an equilibrium between the base (B) and its conjugate acid (BH?), along with hydroxide ions (OH?). The equilibrium constant for this reaction is defined as Kb = [BH?][OH?] / [B]. This concept is fundamental when calculating the concentration of hydroxide ions in a solution containing a weak base.

Buffer Solutions and Conjugate Acid?Base Pairs

When a solution contains both a weak base and its conjugate acid, it can behave as a buffer solution. Buffers resist changes in pH upon the addition of small amounts of acids or bases. The presence of both species allows the application of the Henderson–Hasselbalch equation, which relates pH (or pOH) to the pKa (or pKb) and the ratio of the concentrations of the base and its conjugate acid.

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